A user thanked me for my help but told me that he(/she) cannot accept my answer because he doesn't have enough reputation for that.
Is this possible?
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No, this is not possible. Even question-banned users can edit/accept on their questions.
Hey may have clicked the upvote button instead. Especially if he's on mobile; it's very common to mis-tap on mobile.
Checking out the actual comment being discussed, it looks like the OP doesn't want to accept, since he got a bad "reputation" (not the EXP stuff, the "what others think of you" stuff) for asking it.
You've misinterpreted the OP's comment. To clarify, the OP said:
sorry, You know, I can't do it. I got too bad reputation because of this question ;(
This means the negative reaction to their question makes them unwilling to accept an answer, not that they are technically unable to accept an answer.